You need special tools to remove and reassemble. You also need special tools to measure run-out so you can readjust. Most guys doing this only once or twice in a lifetime farm this job out. AS mentioned above, it is one of the more difficult items to R&R on a C2.
Most guys remove the trailing arms and send them in to a specialist. Some people have the spindles removed with the trailing arm on the car and everything repaired. If your bushings are in good shape and your alignment is good, I'd go the on-the-car route. If not, might as well remove and send them in.
I can see that someone replaced the left spindle on my '65. They did it with the trailing arm ON the car because the spindle/bearing is new and the trailing arm is all dirty with surface rust and my bushing is shot..... dumb.
Brian